Back action cancellation in resolved sideband regime

We consider the simple model of measurement of mechanical oscillator position via Fabry-Pero cavity pumped by detuned laser (end mirror of cavity is mass of oscillator) in resolved sideband regime when laser is detuned from cavity's frequency by frequency of mechanical oscillator $\pmω_m$ and relaxation rate $γ$ of cavity is small: $γ\ll ω_m$. We demonstrate fluctuation back action cancellation in reflected wave. However, it does not allow to circumvent Standard Quantum Limit, the reason of it is the dynamic back action.

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